>Go up to a woman that you feel drawn to and stand there and say "I have to say. I'm very nervous to talk to you but I had to walk over and say hi."
Please don't. That is, unless you have material after this line, which is unlikely unless you are already skilled in chatting up strangers. You'll create an awkward situation. She'll probably give you a forced smile, and then you'll panic because now the you've opened with a sketch line and nothing else to say. I've definitely done this a number of times. I am speaking from the pain of experience.
You'd be better off finding something innocuous you like about her, and why, then opening with that. 'I like your striped socks. Where did you get them?' Then you have something to talk about for a bit.
That aside, I struggle with this too. I just spent the day at a friend's birthday party with 95% new people, and I am socially wiped. My suggestion if you want to progress in the social skills dept: practice. Make time for it.
I wholeheartedly agree with the find-a-new-hobby advice. Salsa class is a _great_ example because in a given night you get ~10-30 interactions with new women when you rotate. It is rapid fire practice. Also rock-climbing. People are friendly and social. I always ask about techniques to climb X, which can lead to a decent convo.
And finally, go to every social thing you are invited to. Everything. Even if you feel shitty and want to hole up with your computer. It will get easier.